# Gelfand spectra in Grothendieck toposes using geometric mathematics

@inproceedings{Spitters2013GelfandSI, title={Gelfand spectra in Grothendieck toposes using geometric mathematics}, author={Bas Spitters and Steven J. Vickers and Sander Wolters}, booktitle={QPL}, year={2013} }

In the (covariant) topos approach to quantum theory by Heunen, Landsman and Spitters, one associates to each unital C*-algebra, A, a topos T(A) of sheaves on a locale and a commutative C*-algebra, a, within that topos. The Gelfand spectrum of a is a locale S in this topos, which is equivalent to a bundle over the base locale. We further develop this external presentation of the locale S, by noting that the construction of the Gelfand spectrum in a general topos can be described using geometric…

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